According to Torricelli's theorem, the velocity of a fluid draining from a hole in a tank is V ≈

1. The velocity of the fluid draining from the hole is given by Torricelli's theorem as $V appro

According to Torricelli's theorem, the velocity of a fluid...

According to Torricelli's theorem, the velocity of a fluid draining from a hole in a tank is $V \approx(2 g h)^{1 / 2},$ where $h$ is the depth of water above the hole, as in Fig. P3.93. Let the hole have area $A_{o}$ and the cylindrical tank have cross-section $\operatorname{area} A_{b} \gg A_{o} .$ Derive a formula for the time to drain the tank completely from an initial depth $h_{o}$.

Transcript

00:01 In this question, you look at basically a tank, right? tank with a hole, right? so let's look at the tank.

00:13 It's something like this, right? the tank has a height somewhere here, and there's a little hole at the bottom, right? there's a hole and this tank, and it has some liquid water, right, inside.

00:25 And so the water initially probably has this height, is a h -0.

00:31 And the cross section of this a tank is ab and the whole has a cross section which is a o right and so you are basically asked how now it will take for this all the those liquid to come out to to get out of this hole right and you know if you at some point at the h the head h is a function of t, right? if you look at how dh over dt, i mean the how h would change, of course, it can be recognized.

01:08 Hedr is going to decrease in, right? it's going to decrease in.

01:11 So it's going to be given by minus how much water comes out, right? so that would be a or times the speed, right? and the speed, the water comes out, right? the water comes out with a speed, which the function of which is a function of h right so h and divide this by a b right so that would be how the head would change right so you can find this to be a or over ab and times vh according to question vh is given by scurlata of 2g h right so that will be and this of course can be actually easily solved, you'll find this.

01:56 So let's rewrite it to be a or squatted to g over a, b times h half, right? so obviously h should be something like, i guess h is going to be something like, all right.

02:15 So you need to actually solve this equation.

02:19 You have, there are many ways to solve this equation actually...

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